In the exercise section I found these 2 sentences:
1- If she could see him she would be proud of him.
2- If you moved away you might not see them again.
I answered that they both are conditionals, but the auto-correcting gave me wrong for the second sentence!!
So please could you help me to stinguish the hypothetical from the conditional??

I'm sorry those answers confused you. We are going to change the exercise so that options 2 and 3 are the same. It will say something like 'The past tense is used to describe hypothetical situations in the present or future. These may be part of a conditional structure.' because really these are the same thing. We'll also change the page so that the explanation is clearer.

It will probably take us a few days to do this. We're very grateful that you took the time to ask us about this. The page will be better because of you!

We're happy to help with questions like this, but in the future please tell us what you think the answer is and why. That way we can help you understand it better.

In this case, 'was' (past simple) is the best form. Sometimes the past continuous works well in a situation like this, but since 'be' isn't used very often in the past continuous, 'was' is the best choice here.

I had doubts about using tense with 'all day'. I always use Past Continuous in such situations. But I've recently heard the version that Present Perfect is possible here, which has confused me a little...
Is it possible?

The answer is that we can't use 'had' in this way! The sentence is not correct and I can only guess that it is a misprint. It is possible to use either 'had given' or 'had had' in this sentence - both are examples of the past perfect using the third forms of the verbs 'give' and 'had', respectively.